Since you have 40 days...u can divide all of it into 4 parts and visit the north, east or central, west and south of India.

Since u are landing in Mumbai...go around the places there first (the posts above have given many nice places to see around in Mumbai...including goa if u intend to be on beaches ..)

Then may be u can move towards north... u can land in Delhi (there are several cheap flights between Mumbai and Delhi)...have an idea of the capital..and from there u can go to near by places like Chandigarh, Jim corbett national park (u can enjoy the loghuts there, u need to book before u go there ...on the way to it is there booking office...I do not remember it offhand but may be if I remember will keep u posted if u are interested... I am not sure if it can be booked online), Ranikhet, Agra... Nainital can be a good hill station...if u like or u can leave it to the south india such as Kodaikanal... Simla in north may be not a good option as it is more of commercialised...Kodaikanal still has that charm...moreover I think it wouldn't be raining there at that time..you can then also go over to Rajasthan specially to Jaipur and Udaipur..

Moving down u can stop by at Panchmarhi in MP (Madhya Pradesh).. if u like to see some heritage of India u can visit Ujjain also.

Coming down to South, you can visit Kodaikanal near Madurai... then Bangalore, Mysore (do go to Vrindavan Gardens there), Ooty and then move on to Kerala...

East I have not mentioned anything as I do not know much about it except for Darjeeling... may be someone here can advice you...

Wish u a comortable and enjoyable holidays...

P.S. If u are planning to travel around by urself...u need to start booking right away as on some flights u can get good discounted rates if u book in advance such as Jetlite...etc. Train ticekets can be booked now 90 days in advance.

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